VCManual.pdf

VauCanSon-G

A package for drawing automata and graphs

User’s manual

Sylvain Lombardy

IGM-LabInfo , Univ. Paris-Est

Jacques Sakarovitch

LTCI, CNRS / TELECOM ParisTech

October 27., 2008

Version 0.4

— ◦ —

VauCanSon-G is a package that allows to draw automata within texts written using

LATEX. It is a set of macros that uses commands of the beautiful PSTricks package, due

to Timothy van Zandt1 and which is part of the current LATEX distribution. VauCanSon-

G is the result of the experience gained in composing the several hundreds of figures in the

book Elements de theorie des automates ([5]) and in several other papers and conferences

slides of the authors.

The design of VauCanSon-G implements the following underlying philosophy:

1. ‘simple’ automata should be described with simple commands.

2. Every element of a figure can easily be given a style (which differs from the implicit

one).

3. The complexity of commands (or the number of things to be remembered to use

them) should gradually grow with the complexity of the figure composed by these

commands.

4. It should be possible to handle the figures both in size and appearance without

modifying them.

The following example2 shows how a simple automaton can be drawn with commands,

in which only the minimal information needed (position and label of states, shape and

label of transitions) is made explicit.

1The maintenance and evolution of PSTricks has now been taken over by H. Voss.2somewhat artificial but which exhibits most of the simple commands.

1

VauCanSon-G manual

p rab

b

a

d

\begin{VCPicture}{(0,-2)(6,2)}

% states

\State[p]{(0,0)}{A} \State{(3,0)}{B} \State[r]{(6,0)}{C}

% initial--final

\Initial{A} \Final{C}

% transitions

\EdgeL{A}{B}{a} \ArcL{B}{C}{b} \ArcL{C}{B}{b}

\LoopN{A}{a} \LoopS{C}{d}

%

\end{VCPicture}

The objectives of VauCanSon-G are achieved by the implicit definition of a large

number of parameters that control the geometry of the figure: size of states, width of

lines, etc. and by the definition of commands that allow to handle and modify these

parameters.

The following pages gives a presentation of VauCanSon-G that gradually introduces

the commands from the basic ones that allow to draw already a good deal of automata to

the more sophisticated ones that are used to modify the internal parameters.

Contents

0 Downloading and using the package 3

1 Basic commands 4

2 Using preset parameters 7

3 Composing a picture 15

4 Parametrized drawing commands 18

5 Modifying and setting the parameters 22

6 Using “plain” PSTricks commands 30

A Version history 31

B Style files 32

Version 0.4 – 2 – October 27., 2008

VauCanSon-G manual

0 Downloading and using the package

The VauCanSon-G package is downloadable from the URL:

/igm.univ-mlv.fr/∼∼∼lombardy/Vaucanson-G/

and consists, beside the present manual, in seven files: the wrapper vaucanson-g.sty, the

main macro file VauCanSon-G.tex, and five other ancillary files3 for options, patches and

colors: VCPref-default.tex, VCPref-slides.tex, VCPref-beamer.tex, VCPref-mystyle.tex,

VCColor-names.def that should all be stored in the user’s texinputs directory.

A LATEX file that will use VauCanSon-G macros should contain the call to the wrap-

per in the preamble:

\usepackage{vaucanson-g}

The VauCanSon-G commands are to be used in a LATEX file and not in a plain TEX

file for it uses the macro \newcommand that does not exist in TEX.

VauCanSon-G is based on the PSTricks package. The knowledge of this macro

package, described in [1], [3, Ch. 4], [4], [6], is not necessary to use the VauCanSon-G

commands.4 On the contrary, VauCanSon-G has somehow be written to save on it. In

particular, the VauCanSon-G commands follow the simple (and rigid) syntax of LATEX

commands concerning the way the arguments are specified, and not the much more flexible

syntax of PSTricks itself.

But the call to PSTricks commands has the consequence that VauCanSon-G com-

mands generate pieces of Postscript files which in turn has two main outcomes5:

• VauCanSon-G is not compatible with pdflatex ;

• the figures produced with VauCanSon-G are not likely to be seen on a DVI viewer:

the space occupied by the figure will appear empty and, in most cases, the labels

will appear at the bottom of it.

VauCanSon-G can be used with the beamer document class to design slides. The

document class should be called with xcolor=pst,dvips options:

\documentclass[xcolor=pst,dvips]{beamer}.

Thus equipped, we may begin.

3Cf. Section 5 for an explanation on the role of these files.4It probably helps in understanding how they are built, and is useful if one wants to make figures that

consists of automata but also contains other graphical elements (cf. Section 6).5which a user should have in mind before sending complaint and request.


VauCanSon-G manual

1 Basic commands

An automaton is a labelled directed graph where some of the vertices, called states, are

distinguished to be initial or final states. The basic commands allow then to define and

to draw states, to give them the quality of being initial or final and to give them labels

as well. They allow to draw transitions between states (that have been defined before);

there are 3 kinds of transitions: (straight) edges, arcs and loops.

These commands have to be put in an environment that defines a picture. All graphical

parameters of these elements (size, line width, etc.) are kept implicit when using these

basic commands.

1.1 The VCPicture environment

\begin{VCPicture}{(x0, y0)(x1, y1)}

. . .

\end{VCPicture}

Defines a box that “encloses” the elements defined in the en-

vironment. Its lower left (resp. upper right) corner has coor-

dinates (x0, y0) (resp. (x1, y1)).

The xi and yi are either length or numbers in which case they represent the corre-

sponding length in centimeter (which is the implicit length unit used in VauCanSon-G).

The length of the box is thus x1 − x0, its height y1 − y0, its baseline point stands at the

middle of the height. As usual in TEX, a picture may well “contain” an element that

actually lays outside of the box.

Note that the environment has only one argument consisting of two point coordinates

enclosed in adjacent parentheses.

1.2 The State commands

States are represented by circles, inside which an information (the Label) can be written.

Every state is given a Name which is used then internally in the figure to describe the

transitions that start from it or end at it.

\State[Label]{(x, y)}{Name} Defines a state with name Name and draws it at the coordi-

nate (x, y) with label Label written inside.

The parameter Label is optional; default value is the empty string. It is written in ‘TEX

mathmode’.

\Initial[Dir]{Name} Makes the state Name initial, i.e. draws an incoming arrow

from the direction Dir to state Name.

\Final[Dir]{Name} Makes the state Name final, i.e. draws an outgoing arrow

from state Name in the direction Dir.


VauCanSon-G manual

The parameter Dir is optional; the possible values are the eight main compass points: n,

s, e, w, ne, nw, se and sw. Default value is w for \Initial, e for \Final.

Many authors, in particular those dealing with automata on infinite words, rather

indicate that a state is final by drawing it with doubleline. The reason why it is not

possible to achieve this result by a sequence of two commands comes from the PSTricks

macros that are called by the VauCanSon-G commands.

\FinalState[Label]{(x, y)}{Name} Same as \State but draws state Name with a doubleline

which is a common way to indicate that a state is final.

p r

r


% states

\State[p]{(0,1)}{A} \State{(2,-1)}{B} \State[r]{(4,1)}{C}

\FinalState[r]{(6,-1)}{D}

% initial--final

\InitialL{A} \Final{A}

\Initial[ne]{B} \Initial[nw]{B}

\Initial[se]{B} \Initial[sw]{B}

\Initial{C} \Final[w]{C} \Initial[n]{D} \Final[s]{D}

%

\end{VCPicture}%

1.3 The Edge commands

Edges, like the other transitions, are oriented from the origin state to the end state. The

left and the right sides of a transition are defined with respect to this orientation, being

the left and the right hand of someone standing on the origin state and following the

transition towards the end state.

\EdgeL[Pos]{Start}{End}{Label}

\EdgeR[Pos]{Start}{End}{Label}

Draws a straight transition from the state Start to the state

End with the label Label on the left side for \EdgeL, on the

right side for \EdgeR.

The parameter Pos is optional. It is a number (0 6 Pos 6 1) that defines the position

of the label on the edge. Default value is .45 and may be used most of the time — this

slight disymmetry gives some “dynamic” to the figure. Explicit value for Pos is used to

avoid collision with other elements of the figure. As for states, the label is written in ‘TEX

mathmode’.


VauCanSon-G manual

A

B

C

D

a

b

c

d

x


% states

\State[A]{(0,0)}{A} \State[B]{(2,-2)}{B} \State[C]{(4,2)}{C}

\State[D]{(6,0)}{D}

% transitions

\EdgeR{A}{B}{a} \EdgeL{A}{C}{b} \EdgeR{B}{D}{c}

\EdgeL{C}{D}{d} \EdgeL{C}{B}{} \EdgeL[.3]{A}{D}{x}

%

\end{VCPicture}

1.4 The Arc commands

Arcs are transitions that link the Start state to the End state with a curved line. The

main parameter of such a curve is the angle made at both ends by the curve with the

straight line that goes from Start to End and it can be oriented to the left or to the right.

In the sequel, the letter X stands for either L or R.

\ArcX[Pos]{Start}{End}{Label}

\LArcX[Pos]{Start}{End}{Label}

Same syntax as \EdgeX .

The starting angle is 15o for ArcX , 30o for LArcX .

Parameter Pos is optional. Default value is .4 .

A

B

C

D

a

b

c

d

a′b′

c′

d′


% states


\State[D]{(6,0)}{D}

%initial-final

\Initial{A} \Final[s]{B} \Final[n]{C}

% transitions

\ArcR{A}{B}{a} \ArcL{A}{C}{b} \LArcR{B}{D}{c} \LArcL{C}{D}{d}

\ArcL{A}{B}{a’} \EdgeR{A}{C}{b’} \EdgeL{B}{D}{c’}

\LArcR{C}{D}{d’}

%

\end{VCPicture}

1.5 The Loop commands

Loops are transitions that link a state to itself, a state which is thus both the origin and

the end of the transition. The two main parameters of such a loop are the opening angle

and the direction of the loop. In the sequel, the letter Y stands for any of the compass

points: N, S, E, W, NE, NW, SE or SW.

\LoopY[Pos]{Name}{Label}

\CLoopY[Pos]{Name}{Label}

Draw a loop around the state Name with label Label.

The direction of the loop is given by Y . The opening of the

loop is 60o for the LoopY commands, 44o for the CLoopY com-

mands.

Parameter Pos is optional. Default value is .25 .


VauCanSon-G manual

A

B

C

D

ew

s

n

sesw

nenw

ew

s

n


% states


\State[D]{(6,0)}{D}

% transitions

\LoopE{A}{e} \LoopW{A}{w} \LoopS{A}{s} \LoopN[.5]{A}{n}

\LoopSE[.5]{B}{se} \LoopSW[.5]{B}{sw}

\CLoopNE[.6]{C}{ne} \CLoopNW[.6]{C}{nw}

\CLoopE{D}{e} \CLoopW{D}{w} \CLoopS{D}{s} \CLoopN[.5]{D}{n}

%

\end{VCPicture}

1.6 An example

This is an automaton with multiplicity in N. The multiplicity of a word u is the square

of the number represented by u in base 2, when a is interpreted as 0 and b as 1.

i q t2b 2b

ba

b2a + 2b

4a

4b


% states

\State[i]{(0,0)}{A} \State[q]{(3,0)}{B} \State[t]{(6,0)}{C}

% initial-final


% transitions

\EdgeR{A}{B}{2b} \EdgeR{B}{C}{2b} \LArcL{A}{C}{b}

\LoopN{A}{a} \LoopS{A}{b} \LoopS[.5]{B}{2a+2b}

\LoopN[.75]{C}{4a} \LoopS[.75]{C}{4b}

%

\end{VCPicture}

2 Using preset parameters

Together with the basic commands, VauCanSon-G gives easy access to two convenient

parameters for drawing automata: global scaling and state size.

2.1 Global scaling

The meticulous reader has noticed that the actual size, mesured for instance by the dis-

tance between the states, is not the one given in the source code. This is because we have

slightly cheated and the source code of the picture is indeed encapsulated in a \VCDraw

command that uses a preset parameter \VCScale as shown below, with no cheating any-

more.

p q\begin{VCPicture}{(0,-1)(3,1)}

\State[p]{(0,0)}{A} \State[q]{(3,0)}{B}

\end{VCPicture}


VauCanSon-G manual

p q

\VCDraw{%


\State[p]{(0,0)}{A} \State[q]{(3,0)}{B}%

\end{VCPicture}}

Frames that appear on figures below are an option of VauCanSon-G that we shall see

later. They point out the effect of the scale.

There is no reason indeed for an author to “program” the drawing of an automaton at the

size it will appear on his, or her, paper. On the contrary, he, or she, is likely to sketch the

figure on a ruled paper at a larger scale, giving the points to be defined integer coordinates.

And then she, or he, will try to put the figure within the text at a reasonable size and

thus would like to scale it.

The parameter \VCScale contains this global scaling factor and is initialized to the

value 0.6 , which corresponds to the command \MediumPicture. Three other commands:

\TinyPicture , \SmallPicture and \LargePicture are available, that set \VCScale to

the values 0.42 , 0.5 and 0.85 respectively.

These command have to be used outside the scope of the VCPicture environment; and

this environment should be called as the parameter of a \VCDraw .

p p p p

\TinyPicture\VCDraw{%

\begin{VCPicture}{(-1,-1)(1,1)}\State[p]{(0,0)}{A}\end{VCPicture}}

\SmallPicture\VCDraw{%


\MediumPicture\VCDraw{%


\LargePicture\VCDraw{%


In the sequel, and unless otherwise stated, all the figure will be given at the \MediumPicture

scale without mentionning the command \VCDraw in the source code.

2.2 State size

There are three preset sizes for the states, that are called by the commands \SmallState,

\MediumState and \LargeState, that call for states of diameter 0.6cm, 0.9cm and 1.2cm

respectively. The implicit size, i.e. the one that states have if no explicit command is

given, is \MediumState. The “small” states are not likely to receive labels, unless their

size are changed by other commands.

A

C

D


% states

\State[A]{(0,0)}{A}

\SmallState\State{(2,-2)}{B}

\MediumState\State[C]{(4,2)}{C}

\LargeState\State[D]{(6,0)}{D}

%

\end{VCPicture}


VauCanSon-G manual

When called outside the scope of the environment \VCPicture the commands \SmallState,

\MediumState and \LargeState set the implicit size of the states in all pictures from that

point on.

A A A

\SmallState

\begin{VCPicture}{(-1,-1)(1,1)}\State[A]{(0,0)}{A} \end{VCPicture}

\LargeState


\MediumState


2.3 Variable size states

One can draw states which will be called variable states and whose width is variable and

fits the width of the label.6 The height of these variable states is fixed by the current

preset state size.

\StateVar[Label]{(x, y)}{Name} Same as syntax as \State.

Note that the current version of VauCanSon-G uses a trick to make these states with

adaptable width. They look like Egyptian cartouches but they are indeed rectangles which

can be observed when transitions reach these states in an oblique way.

Arcs between variable states of different width will look asymmetric and often ungainly.

Other loops than “north” and “south” loops should not be drawn around variable states.

Moreover, in order to draw loops that have the same appearance as loops around standard

states, one should use \LoopVarN or \LoopVarS that have the same syntax as \LoopN or

\LoopS. Another possibility is to call the \VarLoopOn command to make all the subsequent

loops suited to variable states. Switching back to ‘normal’ loops is made by \VarLoopOff.

For the same reason, it is not possible to make a variable state initial or final with

diagonal arrows (ne, nw, se, sw).

6This makes sense for long labels and it may be the case then that the label is not a mathematical

variable or expression any more but simple text. In order to write labels in TEX LR mode, the easiest way

is to write it as the parameter of a \text command, provided the amsmath package has been called in the

preamble.


VauCanSon-G manual

AA AA (ba∗b)∗

AA AA (ba∗b)∗

ab

ca

a

bb

c c

c c

\SmallPicture\VCDraw{\begin{VCPicture}{(0,-3)(8,3)}

% states

\State[AA]{(0,2)}{A} \StateVar[AA]{(2.5,2)}{B}

\StateVar[(b a^{*} b)^{*}]{(7,2)}{C}

\LargeState \StateVar[(b a^{*} b)^{*}]{(7,-2)}{C1}

\State[AA]{(0,-2)}{A1} \StateVar[AA]{(2.5,-2)}{B1}

%

\Initial[n]{B} \Final{C} \Initial[s]{B1} \Final{C1}

%

\EdgeL{A}{B}{a} \ArcL{B}{C}{b} \ArcL{C}{C1}{c} \EdgeL{B1}{C}{a}

\ArcL{A1}{B1}{a} \LArcR{A1}{B1}{b} \LArcR{B1}{C1}{b}

\LoopN{A}{c} \LoopVarN{C}{c}

\LoopS{A1}{c} \VarLoopOn\LoopS{C1}{c}\VarLoopOff

\end{VCPicture}}

There exists7 also a \FinalStateVar command, with the same syntax as \StateVar and

which draws a variable state with double line, (independently of the current drawing style

for the state), exactly in the same way as does \FinalState.

2.4 Very small states

There is actually a fourth size for states, called very small states. To define such a state

one uses the command \VSState with the same syntax as \State. However, it is not

possible, of course, to put a label inside such a state.

A

a1

a2

a3

b1

b2

b3

\begin{VCPicture}{(-3,-3)(3,3)}

% states

\State[A]{(0,0)}{A}

\VSState{(-2,2)}{G1} \VSState{(-2,0)}{G2} \VSState{(-2,-2)}{G3}

\VSState{(2,2)}{D1} \VSState{(2,0)}{D2} \VSState{(2,-2)}{D3}

\EdgeL{G1}{A}{a_1} \EdgeL{G2}{A}{a_2} \EdgeL{G3}{A}{a_3}

\EdgeL{A}{D1}{b_1} \EdgeL{A}{D2}{b_2} \EdgeL{A}{D3}{b_3}

\end{VCPicture}}

2.5 Miscellaneous

A few commands allow to tune the drawing of an automaton without going to precise

mastering of the parameters involved in the commands and that we shall describe in

section 4.

Dimmed states and transitions

\DimState \DimEdge

\RstState \RstEdge

Draw states and transitions and their respective labels in gray.

Restore the normal style.

May be used for instance in order to indicate the non accessible part of an automaton.

7Since version 0.3 only.

Version 0.4 – 10 – October 27., 2008

VauCanSon-G manual

A

B

C

D

a

b

c

d

a′b′

c′

d′


% states


\DimState \State[D]{(6,0)}{D}

%initial-final

\Initial{A} \Final[s]{B} \Final[n]{C}

% transitions

\ArcR{A}{B}{a} \ArcL{A}{C}{b}

\DimEdge \LArcR{B}{D}{c} \LArcL{C}{D}{d} \RstEdge

\ArcL{A}{B}{a’} \EdgeR{A}{C}{b’}

\DimEdge \EdgeL{B}{D}{c’} \LArcR{C}{D}{d’}

%

\end{VCPicture}

Double lines

\StateLineDouble \EdgeLineDouble

\StateLineSimple \EdgeLineSimple

Draw states and transitions with double lines.

Draw states and transitions with simple lines.

May be used for emphasize transitions or states of an automaton.

A

B

C

D

a

b

c

d

a′b′

c′

d′


% states

\State[A]{(0,0)}{A} \State[B]{(2,-2)}{B}

\StateLineDouble \State[C]{(4,2)}{C}

\StateLineSimple \State[D]{(6,0)}{D}

%initial-final

\Initial{A} \Final[s]{B}

% transitions


\LArcR{B}{D}{c} \LArcL{C}{D}{d}

\ArcL{A}{B}{a’} \EdgeLineDouble \EdgeR{A}{C}{b’}

\EdgeLineSimple \EdgeL{B}{D}{c’} \LArcR{C}{D}{d’}

%

\end{VCPicture}

The command \FinalState{(x, y)}{p} is equivalent to the sequence

\StateLineDouble \State{(x, y)}{p} \StateLineSimple if the current implicit mode is

\StateLineSimple , it is equivalent to \State{(x, y)}{p} in the other case.

Hiding states

\HideState

\ShowState

Cancel the drawing of states.

Active the drawing of states.

May be useful for drawing slides that will be overlayed.8

8We began to write the package when overhead projectors were still of common usage. . .

Version 0.4 – 11 – October 27., 2008

VauCanSon-G manual

q2b 2b

ba

b2a + 2b

4a

4b


% states

\HideState

\State[i]{(0,0)}{A} \State[t]{(6,0)}{C}

\ShowState

\State[q]{(3,0)}{B}

% initial-final


% transitions



\LoopN[.75]{C}{4a} \LoopS[.75]{C}{4b}

%

\end{VCPicture}

Reverse transitions

\ReverseArrow

\StraightArrow

Exchange the origin and the end of a transition.


May be useful for modifying a part of a figure that had already been written.

A

B

C

D

a

b

c

d

a′

b′

c′d′


% states


\State[D]{(6,0)}{D}

% transitions

\Final[s]{B}

\ArcR{A}{B}{a} \ArcL{A}{C}{b} \LArcR{B}{D}{c} \LArcL{C}{D}{d}

\ReverseArrow

\Initial{A} \Final[n]{C}

\ArcL{A}{B}{a’} \EdgeR{A}{C}{b’} \EdgeL{B}{D}{c’}

\LArcR{C}{D}{d’}

%

\end{VCPicture}

Edge border

\EdgeBorder

\EdgeBorderOff

Draw edges with a white border on each side.


May be used to make more readable a picture in which many arrows cross each other. The

order in which the edges are drawn becomes then meaningfull.

Version 0.4 – 12 – October 27., 2008

VauCanSon-G manual

A

B

C

D

E

Fa

b

b

a

d

c


% states

\State[A]{(0,1)}{A} \State[B]{(3,2)}{B} \State[C]{(6,1)}{C}

\State[D]{(0,-1)}{D} \State[E]{(3,-2)}{E} \State[F]{(6,-1)}{F}

% transitions

\EdgeR{A}{E}{a} \EdgeL[.8]{D}{B}{b} \EdgeR[.7]{B}{E}{b}

%

\EdgeBorder

\EdgeL[.35]{A}{F}{a} \EdgeR[.3]{E}{C}{d}

\EdgeBorderOff

\EdgeL{B}{F}{c}

\end{VCPicture}

Forth and back offset Normally, an edge lays on the line that links the center of

the start and end states. Which forbid to have two straight edges in opposite directions

between states.

\ForthBackOffset

\RstEdgeOffset

Shift the edge on the left handside.


A B C

A B C

a b

b

a b

b


% states

\State[A]{(0,1)}{A} \State[B]{(3,1)}{B} \State[C]{(6,1)}{C}

\LargeState

\State[A]{(0,-1)}{A1} \State[B]{(3,-1)}{B1}

\State[C]{(6,-1)}{C1}

% transitions

\EdgeL{A}{B}{a}

\ForthBackOffset \EdgeL{B}{C}{b} \EdgeL{C}{B}{b}

\RstEdgeOffset \EdgeL{A1}{B1}{a}

\ForthBackOffset \EdgeL{B1}{C1}{b} \EdgeL{C1}{B1}{b}

\end{VCPicture}

Zigzag edges

\ZZEdgeL[Pos]{Start}{End}{Label}

\ZZEdgeR[Pos]{Start}{End}{Label}

Draws a “zigzag” transition from the state Start to the state

End with the label Label on the left or the right side.

A

B

C

a

b

c

d

b


% states


\VSState{(6,0)}{D}

% transitions

\EdgeR{A}{B}{a} \EdgeL{A}{C}{b} \EdgeR{B}{D}{c}

\ZZEdgeL{C}{D}{d} \ZZEdgeR{C}{B}{b}

%

\end{VCPicture}

Lining up By default, labels of states are centered. When states are aligned, it may

happen that this seems ungainly. The following command solves this problem.

Version 0.4 – 13 – October 27., 2008

VauCanSon-G manual

\AlignedLabel

\FloatingLabel

Put labels of states on a virtual baseline.

Center the label of states vertically.

Default option is \FloatingLabel.

p b a

p b a

ab

c

ab

c


% states

\State[p]{(0,0)}{A} \State[b]{(3,0)}{B} \State[a]{(6,0)}{C}

\AlignedLabel

\State[p]{(0,-3)}{A1} \State[b]{(3,-3)}{B1}

\State[a]{(6,-3)}{C1}

%transitions

\EdgeL{A}{B}{a} \ArcL{B}{C}{b} \ArcL{C}{B}{c}

\EdgeL{A1}{B1}{a} \ArcL{B1}{C1}{b} \ArcL{C1}{B1}{c}

%

\end{VCPicture}%

The command \Point This commands is a direct translation of a command from

PSTricks.

\Point{(x, y)}{Name} Sets a point with name Name at the coordinate (x, y).

This command does not draw any point. With PSTricks, and thus with VauCanSon-

G, any line or curve must be drawn between two predefined objects. That is the aim of

\Point. For instance, initial and final arrows are drawn with this trick: any time a state

is defined, eight points are silently and implicitely defined around it.

2.6 Writing composite labels

Some useful tools are proposed to write composite labels on arrows.

\IOL{Input}{Output} Produces the string Input|Output, useful when one draws

transducers. This allows to modify the way it is done by

redefining command \IOL.

\StackXLabels{Label1}{Label2}

\StackXLabelsP{Label1}{Label2}

\LineXLabelsP{Label1}{Label2}

In these commands, X equals Two or Three. In the later case,

commands have obviously three arguments.

\StackXLabels gives a vertical arrangement of labels,

whereas \StackXLabelsP inserts symbols + between them.

\LineXLabelsP is the horizontal version of \StackXLabelsP;

it can be redefined in order to change symbols, for instance.

The following automaton is the right sequential transducer that realizes the addition in

base 2.

Version 0.4 – 14 – October 27., 2008

VauCanSon-G manual

0 1|1

0 |0+

1 |1

1 |0 + 2 |12 |0

0 |1


% states

\State[0]{(0,0)}{A} \State[1]{(3,0)}{B}

\Initial[n]{A}

\Final[s]{A} \FinalR{e}{B}{\IOL{}{1}}

%transitions

\LoopW[.5]{A}{\StackTwoLabelsP{\IOL{0}{0}}{\IOL{1}{1}}}

\LoopN[.7]{B}{\LineTwoLabelsP{\IOL{1}{0}}{\IOL{2}{1}}}

\ArcL{A}{B}{\IOL{2}{0}}

\ArcL{B}{A}{\IOL{0}{1}}

%

\end{VCPicture}

3 Composing a picture

The commands described above allow to define most of the figures representing automata

in any textbook or technical paper. Before turning to more sophisticated commands that

are used for less than 5 percent of the elements and that appear in less than 10 percent of

the figures, let us turn to few commands that help in composing the figures.

3.1 Structuring the automaton: The VCPut command

In many automata, a same pattern in states, and also in edges, is reproduced several

times in the figure. The idea is not to try to “program” these regular patterns but to

allow the use of the “copy-and-paste” operations in the source file as much as possible,

with minimum corrections afterwards. This will be achieved easily with the help of the

command \VCPut.

\VCPut{(x,y)}{ instructions. . . } Translates the result of the instructions by the vector (x, y).

Note that this command is taken directly from PSTricks but uses VauCanSon-G’s syn-

tax.

Of course the commands that are to be put as the second argument of \VCPut are the

defining states commands, with possibly other \VCPut inside. The structuration of the

figure via the use of \VCPut commands does not only save typing. It makes also easier

the tuning of the figure, and the reusability of its parts.

In the example below, the two \VCPut are used to place the two parts of the automaton.

Version 0.4 – 15 – October 27., 2008

VauCanSon-G manual

j r

s u

b

a + b 2a + 2b

b

2a + 2b 4a + 4b

bbb


\VCPut{(0,3)}{\State[j]{(0,0)}{A1} \State[r]{(3,0)}{B1}}

\VCPut{(3,0)}{\State[s]{(0,0)}{A2} \State[u]{(3,0)}{B2}}

%

\Initial{A1} \Final{B2}

\EdgeL{A1}{B1}{b} \LoopN[.5]{A1}{a+b} \LoopN[.5]{B1}{2a+2b}

\EdgeR{A2}{B2}{b} \LoopS[.5]{A2}{2a+2b} \LoopS[.5]{B2}{4a+4b}

\EdgeR{A1}{A2}{b} \EdgeL{B1}{B2}{b} \EdgeL{A1}{B2}{b}

%

\end{VCPicture}

The \VCPut command can also be used to rotate a figure by using an optional parameter.

\VCPut[r]{(x,y)}{ instructions. . . } Rotate the result of the instructions with angle r and cen-

ter (0, 0) and then translate it by the vector (x, y).

(0, 0) A

90o

C

r

t\begin{VCPicture}{(-1,-1)(5,4)}

\StateVar[(0,0)]{(0,0)}{O}

\State[A]{(3,0)}{A}

\VCPut[90]{(0,0)}{\StateVar[90^o]{(3,0)}{B}}

\VCPut[90]{(4,0)}{\State[C]{(3,0)}{C}}

\LArcR{A}{B}{r} \EdgeL{B}{C}{t}

\end{VCPicture}

The default option is that labels of states (except those of variable states) are put in a

horizontal position (\RigidLabel), but the command \SwivelLabel makes them rotate

with the figure.

1a

2

a

b

3a

b4

a

5a

6

a

b

7

a

b

8

9

b

b

bb

b

a

a


\SwivelLabel

\State[1]{(4,0)}{A1}\LoopE{A1}{a}

\VCPut[40]{(0,0)}{%

\State[2]{(4,0)}{A2}\LoopE{A2}{a}\ArcR{A1}{A2}{b}}

\VCPut[80]{(0,0)}{%


\VCPut[120]{(0,0)}{\State[4]{(4,0)}{A4}\LoopE{A4}{a}}

\VCPut[160]{(0,0)}{\State[5]{(4,0)}{A5}\LoopE{A5}{a}}

\RigidLabel

\VCPut[200]{(0,0)}{%


\VCPut[240]{(0,0)}{%


\VCPut[280]{(0,0)}{\State[8]{(4,0)}{A8}}

\VCPut[320]{(0,0)}{\State[9]{(4,0)}{A9}}

\ArcR{A3}{A4}{b} \ArcR{A4}{A5}{b}

\ArcR{A7}{A8}{b} \ArcR{A8}{A9}{b} \ArcR{A9}{A1}{b}

\LoopL{A8}{280}{a} \LoopL{A9}{320}{a}

\end{VCPicture}

One can notice that \RigidLabel only acts on labels of states. To draw arcs with

“rigid” labels, commands have to be written outside \VCPut. We shall see later how to

deal with the command \LoopL in order to give any orientation to loops without using

\VCPut.

Version 0.4 – 16 – October 27., 2008

VauCanSon-G manual

3.2 Using separate files

In order to use several times the same figure in the same or in different papers, or even,

as we shall see in the next section, in two different contexts such as in a paper and in a

slide for a talk, it is convenient to have the figure written into a file and imported in the

main LATEX source file. This can be handled by the following macros.

\VCCall{FileName} Calls the file FileName and apply the \VCScale.

\SetVCDirectory{Directory} Sets to Directory the directory where the file FileName will

be taken by the macro \VCCall . Set to the current directory

by default. Usual Unix syntax is used to name directories.

\ShowName \HideName Sets or unsets a flag that controls the printing of FileName

besides the figure drawn by \VCCall.

For the example below, the following lines have been saved in the file TwoStates.tex:


\State[p]{(0,0)}{A} \State[q]{(3,0)}{B}%

\ArcL{A}{B}{b} \LArcL{B}{A}{a} \LoopE{B}{a}

\end{VCPicture}

\VCCall applies the same parameters to figures described in files as \VCDraw does.

p qb

a

a

TwoStates p qb

a

a

\VCCall{TwoStates}

\SmallPicture \ShowName

\VCCall{TwoStates}

3.3 Frame and grid

Two macros that help placing the figure in the page, and the states in the figure.

\ShowFrame \HideFrame Sets or unsets a flag that controls the drawing of the bound-

ing box which is defined by the parameter of the \VCPicture

environment.

\ShowGrid \HideGrid Sets or unsets a flag that controls the drawing of a grid inside

the bounding box which is defined by the parameter of the

\VCPicture environment.

Default settings are \HideFrame and \HideGrid .

-1 0 1 2 3 4-1

0

1

p qb

a

a\ShowFrame \ShowGrid \VCCall{TwoStates}

Version 0.4 – 17 – October 27., 2008

VauCanSon-G manual

3.4 The grid scale

This parameter controls the value of the PSTricks unit length. As values that define the

size of states and the width of lines are given with fixed units (as cm or pt), they are not

modified by this parameter. However, the scale of the grid on which they are put, i.e. the

distance between each other is modified by grid scale. This parameter is actually the first

(optional) argument of \VCDraw or \VCCall.

The following example is the figure of Subsection 1.6 with another grid scale:

i q t2b 2b

ba

b2a + 2b

4a

4b

\VCDraw[.7]{%


% states


% initial-final


% transitions



\LoopN[.75]{C}{4a} \LoopS[.75]{C}{4b}

\end{VCPicture}

}

We can call TwoStates with another grid scale.

-1 0 1 2 3 4-1

0

1

p qb

a

a\ShowFrame \ShowGrid \VCCall[1.5]{TwoStates}

4 Parametrized drawing commands

In the sequel, the letter X stands for either L or R.

4.1 Parametrized loops

One can draw loops around state with any direction.

\LoopX[Pos]{Direction}{Name}{Label}

\CLoopX[Pos]{Direction}{Name}{Label}

Draw a loop around the state Name in direction Direction,

which is an angle with respect to east, with label Label.

As the label is placed outside the loop, \LoopL is reversed

with respect to \LoopR. The opening of the loop is 60o for the

LoopX commands, 44o for the CLoopX commands.

Version 0.4 – 18 – October 27., 2008

VauCanSon-G manual

i q t2b 2b

ba

b 2a + 2b

4a

4b


% states


% initial-final


% transitions


\LoopR{120}{A}{a} \LoopL{-120}{A}{b} \LoopS[.5]{B}{2a+2b}

\LoopL[.5]{60}{C}{4a} \LoopR[.5]{-60}{C}{4b}

%

\end{VCPicture}%

4.2 Parametrized arcs

\VArcX[Pos]{arcangle=x,ncurv=v}{Start}{End}{Label}

Draw an arc from Start to End with la-

bel Label, with a starting angle x and an

eccentricity v.

The starting angle is defined by the parameter arcangle=x and is measured, going to the

left if X=L, to the right if X=R, from the line that goes from Start to End, called the base

line. The parameter ncurv is the ‘eccentricity’ of the arc and some how measures the

distance between the center of the arc and the base line as one can observe on the figure

below.

The first (non optional) parameter of \VArcX contains PSTrick’s parameters, written

with PSTrick’s syntax: they are separated by a comma and there must be no space inside

the braces that contains them. All these parameters are optional, but this first parameter

of \VArcX itself is not an optional argument, which means that this command must always

have four arguments (and possibly an optional one):

\VArcL{arcangle=15}{A}{B}{x}

\VArcL{ncurve=1}{A}{B}{x}

\VArcL{}{A}{B}{x}

are syntactically correct commands.

Default value for arcangle is the same as for \LArc, whereas the default ncurv value is 1.

A B0.2

0.8

2

6

60

90120


% states

\LargeState

\State[A]{(-2,0)}{A}

\State[B]{(2,0)}{B}

%transitions

\VArcR[.5]{arcangle=45,ncurv=.2}{A}{B}{0.2}

\VArcL[.5]{arcangle=45,ncurv=.8}{A}{B}{0.8}

\VArcL[.5]{arcangle=45,ncurv=2}{A}{B}{2}

\VArcR[.5]{arcangle=45,ncurv=6}{A}{B}{6}

\VArcL{arcangle=-60}{A}{B}{60}

\VArcR{arcangle=-90}{A}{B}{90}

\VArcR[.2]{arcangle=-120}{A}{B}{120}

%

\end{VCPicture}

Version 0.4 – 19 – October 27., 2008

VauCanSon-G manual

4.3 General curve

\VCurveX[Pos]{angleA=x,angleB=y,ncurv=v}{Start}{End}{Label}

Draw a curve from Start to End

with label Label, starting with an

angle x, arriving with an angle y

and with an eccentricity v.

A (Bezier) curve, computed by PSTricks with the three parameters: the starting angle

fixed by angleA=x, the ending angle fixed by angleB=y, and the eccentricity ncurv=v.

The two angles are measured, as trigonometric angles are, from the East direction and

counterclockwise. The syntax of these parameters is PSTricks’s and they are optional,

as in \VArcX. Default values for angleA and angleB are respectively 0 and 180; ncurv is

fixed by default to 1.

A B C

1

0.5

2

b c

d


%states

\State[A]{(-3,0)}{A}

\State[B]{(0,0)}{B}

\State[C]{(3,0)}{C}

%transitions

\VCurveL{angleA=90,angleB=135}{A}{B}{1}

\VCurveR[.5]{angleA=90,angleB=135,ncurv=.5}{A}{B}{0.5}

\VCurveL{angleA=90,angleB=135,ncurv=2}{A}{B}{2}

\VCurveR[.6]{angleA=-80,angleB=175}{A}{B}{b}

\VCurveR[.6]{angleA=-80,angleB=175}{A}{C}{c}

\VCurveL{angleB=20,angleB=160}{B}{C}{d}

\end{VCPicture}

4.4 Transitions labelling

Initial and final arrows with a label When one deals with tranducers, or automata

with multiplicity, one may need to put some labels on initial or final arrows.

\InitialL[Pos]{Dir}{Name}{Label}

\InitialR[Pos]{Dir}{Name}{Label}

Makes the state Name initial and writes Label on the left or

the right size of the incoming arrow.

\FinalL[Pos]{Dir}{Name}{Label}

\FinalR[Pos]{Dir}{Name}{Label}

Makes the state Name final and writes Label on the left or

the right size of the outgoinging arrow.

Here, the parameter Dir is not optional. Whereas, there is an optional parameter Pos

that defines the position of the label on the arrow. Its default values is fixed to 0.1 (resp.

0.9) for initial (resp. final) arrows. The label is thus written far enough of the state.

Independant labelling of transitions There exists commands to label transitions

that have not been labeled yet or to put a second label on them. These commands must

directly follow the definition of the transition that will be labeled.

Version 0.4 – 20 – October 27., 2008

VauCanSon-G manual

\LabelL[Pos]{Label}

\LabelR[Pos]{Label}

Puts a label on the previous transition. The default position

of the label is the same as for edges.

A B

C D

u

ϕ(u) = 3

v

a

b

c


\State[A]{(-2,1)}{A} \State[B]{(2,1)}{B}

\State[C]{(-2,-1)}{C} \State[D]{(2,-1)}{D}

%

\EdgeL{A}{B}{u} \LabelR{\varphi(u)=3}

\LArcR{D}{C}{} \LabelL{v}

\VCurveL[.3]{angleA=45,angleB=-45}{B}{D}{a}

\LabelL[.5]{b} \LabelL[.7]{c}

\end{VCPicture}

4.5 Miscellaneous

Loops on variable states Instead of using \VarLoopN or \VarLoopS, one can modify

parameters of loops to draw, for instance, many loops on variable states. As usual, these

loops may be drawn on the south or north side of the states only.

\VarLoopOn

\VarLoopOff

Modifies parameters in order to draw loops around variable

states.

Restore the normal style of loops.

Command \LoopVarN is equivalent to the sequence \LoopVarOn \LoopN \LoopVarOff.

Saving memory In default mode, the call to a \State command defines eight additional

points, that allow then to draw initial and final arrows in the prescribed compass direction.

In case of large figures, with many states, this ought to lead to an overflow of TEX memory.

This is the reason why one can define states without any additional point.

\PlainState

\FullState

Draw states with no additional points.

Draw states with eight points to draw initial or final arrows.

Of course, when in \PlainState mode, one can define states with additional points.

\IFState[Label]{(x, y)}{Name}

\IFXState[Label]{(x, y)}{Name}

Draws a state with four points (n, s, e, w).

Draws a state with eight points (n, s, e, w, ne, se, nw, sw).

In \PlainState mode, one should not apply an \Initial or a \Final command to a

state defined by \State. Likewise, these commands can be only used for \IFState with

directions n, s, e and w.

Note that even when in \FullState mode, variable states defined by \StateVar have

the same four additional points as \IFState.

Version 0.4 – 21 – October 27., 2008

VauCanSon-G manual

5 Modifying and setting the parameters

The reason why the commands in VauCanSon-G are simple and concise is that all the

parameters that control the geometry (size, angles, . . . ) and the drawing (line width,

line style, line color, . . . ) of the states and transitions in an automaton are preset by

VauCanSon-G and can be kept implicit. But there are two instances where a user may

want to modify these preset values.

The first case is when one needs to tune a parameter in order to make the figure more

readable, or nicer. Such a case has already been considered in sections 1.3, 1.4 and 1.5,

where the parameter Pos that controls the position of the label of a transition along the

edge has been modified with an optional argument. The parameters that will be considered

in this section are not optional parameters of already defined commands but parameters

that are set with their own commands.

The other case where a user will change the implicit parameters of a figure or, more

likely, of a set of figures, is when he (or she) will be in the position to change completely

the “style” of the drawing. For instance, a same set of figures may be used in a paper and

in a series of slides for the presentation of the paper. Of course, the figures have to be

set at a larger scale, probably in colour, and possibly with different relative sizes of the

elements.

We begin with the description of the options for the latter case, which is by far simpler.

We then explain the syntax convention taken to coin the names of the many commands

that control the many parameters. Then comes the list of these parameters, for scaling

first, then for states, for transitions, and finally for the fine tuning of some details of the

drawing.

5.1 Style files

The package VauCanSon-G is loaded with default values that are all set up in the file

VCPref-default.tex . The package comes with two other styles, in particular one for

drawing slides. The normal way of using the different style files is to call the wrapper

vaucanson-g with an option:

\usepackage[option]{vaucanson-g}The default option is default; the other possible options are

slides, beamer and mystyle.

Although it is not the normal usage, it is also possible to change style in the course of

the text by loading a style file with an \input command. In this case, it is recommended

to reset all parameters by calling VCPref-default.tex.

Version 0.4 – 22 – October 27., 2008

VauCanSon-G manual

p qb

a

a

p qb

a

a

p qb

a

a

p q

b

a

a

\usepackage{vaucanson-g}

...

\VCCall{TwoStates}

...

\usepackage[slides]{vaucanson-g}

...

\VCCall{TwoStates}

...

\usepackage[beamer]{vaucanson-g}

...

\VCCall{TwoStates}

...

...

\input{VCPref-default} % gets back to default values

\input{VCPref-mystyle}

\VCCall{TwoStates}

By editing the files VCPref-mystyle, VCPref-beamer or VCPref-slides, and giving the

parameters the values he (or she) thinks more appropriate, a user may easily build his

(or her) own style for drawing automata. Modifying directly VCPref-default, although

possible, is not necessarily a good idea. By cut, editing and paste, it is not difficult create

many style files, and even, with an easy modification of the wrapper itself to make them

possible options. The content of these style files are described in the following subsections.

VCPref-slides, VCPref-beamer and VCPref-mystyle are given at Appendix B.

5.2 Syntax of parameter settings

The set of values of all parameters defines a style of figures. Most of parameters, e.g.

\StateLineColor which defines the color of the line that delimits a state, may be given a

temporary value, within a figure, without changing the style. These parameters are dealt

with by means of 3 different commands:

\ChgParam{ Val } Gives the new value Val to \Param.

\RstParam Restores the style value in \Param.

\SetParam{ Val } Sets the style value for \Param to Val .

The command \SetParam can be called outside a \VCPicture environment, in which case

it will be effective in all subsequent figures, until a new setting of the same parameter. Its

natural place, if it is considered as a modification of the style, is in the preamble, after

the call to the package VauCanSon-G. If the command \SetParam is called inside a

\VCPicture environment, its effect will be restricted to that figure.

Such parameters will be called adjustable parameters in the sequel.

Version 0.4 – 23 – October 27., 2008

VauCanSon-G manual

Note that in the case where \Param is a value (a length or a scale), the value of Val in

\ChgParam{Val} is a coefficient which is applied to the style value of \Param defined with

\SetParam{Val}. Therefore, in this case, \RstParam is equivalent to \ChgParam{1}.

The other parameters, as those that define the “dimmed” style, are called preset pa-

rameters.

There is finally a class of parameters that fall in between the adjustable and the preset

ones, those for which several values are “preset” but that can be given other values. These

parameters will be called multivalued preset parameters.

5.3 Scale parameter (Multivalued preset parameter)

\FixVCScale{Scale} Sets \VCScale to Scale.

The commands \MediumPicture, \SmallPicture, \TinyPicture and \LargePicture

set \VCScale to the values \MediumScale, \SmallScale, \TinyScale and \LargeScale

respectively. Their values are

\TinyScale \SmallScale \MediumScale \LargeScale

0.42 0.5 0.6 0.85

These preset values can be modified by a \renewcommand.

5.4 State parameters

State diameter (Multivalued preset parameter) This parameter controls, via the

commands \MediumState, \SmallState or \LargeState the value of a number of other

preset parameters.

\FixStateDiameter{Diam} Sets the state diameter to Diam (Diam is a length) until the

next call to a \ZState command, or to the next figure if called

inside a \VCPicture.

Preset diameter sizes are:

\VerySmallState \SmallState \MediumState \LargeState

0.3cm 0.6cm 0.9cm 1.2cm

These values can be modified by a \renewcommand. However, as commands that call

these parameters deal also with other parameters as the eccentricity of loops or the size of

initial and final arrows, changing these values without modifying the other ones can lead

to an ungainly result.

The shape of a normalized automaton can be drawn in the following way:

Version 0.4 – 24 – October 27., 2008

VauCanSon-G manual

Ai t


\FixStateDiameter{5cm} \ChgStateLabelScale{3}

\State[{\cal A}]{(0,0)}{A}

\MediumState \RstStateLabelScale

\State[i]{(-4,0)}{I} \State[t]{(4,0)}{T}

\VSState{(-1,-1)}{P1} \VSState{(1,-1)}{Q1}

\VSState{(-1,1)}{P2} \VSState{(1,1)}{Q2 ]

\VSState{(-1.4,0)}{P3} \VSState{(1.4,0)}{Q3}

\Initial{I} \Final{T}

%

\EdgeL{I}{P1}{} \EdgeL{I}{P2}{} \EdgeL{I}{P3}{}

\EdgeL{Q1}{T}{} \EdgeL{Q2}{T}{} \EdgeL{Q3}{T}{}

\end{VCPicture}

State adjustable parameters Each following parameter can be modified by the

command \ChgParameter. The style value can be restored by \RstParameter and one

can set the style value with \SetParameter.

Parameter Default value Possible values

StateLineStyle solid dashed, dotted, none

StateLineWidth 1.8pt

StateLineColor black red, lightgray, . . .

StateLabelColor black blue, Salmon, . . .

StateLabelScale 1.7

StateFillStatus solid vlines, hlines, crosshatch, none

StateFillColor white green, Purple, . . .

As it has been previously noticed, the argument of \ChgStateLineWidth is not a

length but a coefficient applied to the style width. For instance, with the default value of

StateLineWidth, after \ChgStateLineWidth{2} edges will be drawn with a 3.6pt width.

When pictures are drawn to scale \VCScale that is set to 0.6, printing state labels

with scale 1.7 makes them to be as large as characters of the text. As for line width,

\ChgStateLabelScale{.5} sets the label scale to 0.85 that make then twice smaller than

characters of the text (because of \VCScale).

Version 0.4 – 25 – October 27., 2008

VauCanSon-G manual

State preset parameters They deal with the definition of “dimmed” states.

Parameter Default value

DimStateLineStyle solid

DimStateLineColor gray

DimStateLineCoef 1

DimStateLabelColor gray

DimStateFillColor white

DimStateLineCoef is a coefficient that is applied to StateLineWidth in drawing dimmed

states. It might be larger than 1 to compensate optical effects when DimStateLineStyle is

dashed or dotted.

The style of dimmed states can be fixed by the command

\FixDimState{LineStyle}{LineColor}{LineCoef }{LabelColor}{FillColor}.

In mode StateLineDouble or when one uses the command \FinalState, two parame-

ters give the width of each of both lines and the distance between them. These values are

coefficients that are applied to StateLineWidth.


StateLineDblCoef 0.6

StateLineDblSep 0.4

These values can be fixed by the command \FixStateLineDouble{Coef }{Sep}.

5.5 Transition parameters

Edge adjustable parameters Each following parameter can be modified by the

command \ChgParameter. The style value can be restored by \RstParameter and one

can set the style value with \SetParameter.

Parameter Default value Possible values

EdgeLineStyle solid dashed, dotted, none

EdgeLineWidth 1pt

EdgeLineColor black many colours

EdgeLineDblStatus false true

EdgeNodeSep 0pt

EdgeLabelColor black many colours

EdgeLabelScale 1.7

EdgeLabelSep 3.5pt

Version 0.4 – 26 – October 27., 2008

VauCanSon-G manual

As for states, the argument of \ChgEdgeLineWidth is a coefficient applied to the style

line width.

The parameter EdgeNodeSep defines a distance between the begining, and the end, of

a transition and the state it starts from and arrives to. The default value is 0pt, that

is, no distance at all; but it may be the case, especially when there is no line around the

state that one may want to increase the distance between the transition and the label of

the state.

The parameter EdgeLabelSep controls the distance between the box that contains the

label of the transition (built by LATEX) and the transition.

Edge preset parameters A first class of preset parameters deals with the definition

of “dimmed” edges.


DimEdgeLineStyle solid

DimEdgeLineColor gray

DimEdgeLineCoef 1.2

DimEdgeLabelColor gray

The style of dimmed edges can be fixed by the command

\FixDimEdge{LineStyle}{LineColor}{LineCoef }{LabelColor}.

The style of the border of edges (in mode \EdgeBorder), is defined by two parameters :


EdgeLineBorderCoef 2

EdgeLineBorderColor white

\EdgeLineBorderCoef is a coefficient applied to \EdgeLineWidth, that gives the width

of the border.

The style of borders of edges can be fixed by the command \FixEdgeBorder{Coef }{Color}.

The width of the double line of (in mode EdgeLineDouble), is defined by two param-

eters, that give the width of each of both lines and the distance between them. These

values are coefficients that are applied to EdgeLineWidth.


EdgeLineDblCoef 0.5

EdgeLineDblSep 0.6

These values can be fixed by the command \FixEdgeLineDouble{Coef }{Sep}.

Version 0.4 – 27 – October 27., 2008

VauCanSon-G manual

5.6 Advanced parameters

These parameters can be changed by using the usual command \renewcommand (or \setlength,

when the parameter is a length).

As it has already be mentionned, the preset commands that set the diameter of states

control parameters for drawing edges (the length of initial and final arrows or the curvature

of loops). Their values are:

X \ArrowOnX \LoopOnX \CLoopOnX

LargeState 1.3 5.8 6

MediumState 1.5 5.8 8

SmallState 1.7 5.8 12

VariableState 5.1 5.2

VerySmallState 5 15

ArrowOnX is the coefficient that is applied to the radius of the state to obtain the

length of initial or final arrows. LoopOnX and CLoopOnX is the eccentricity of loops and

closed loops respectively.

Another parameter determines whether the dimension of states refer to the middle,

the inner or the outer side of the boundary. There exist one parameter for classical states

and one for states with double line:


\StateDimen outer

\StateDblDimen middle

The possible values are inner, outer or middle.

-1 0 1 2 3 4 5 6-1

0

1

2

\ShowGrid

\VCDraw{%


\ChgStateLineWidth{5}

\FixStateDiameter{1cm}

\renewcommand{\StateDimen}{inner}

\State{(0.5,0.5)}{I}

\renewcommand{\StateDimen}{middle}

\State{(2.5,0.5)}{M}

\renewcommand{\StateDimen}{outer}

\State{(4.5,0.5)}{O}

\end{VCPicture}}

\HideGrid

Transition adjustable geometric parameters All these parameters are adjustable.

That means there exist commands as \SetParameter, \ChgParameter and \RstParameter.

Arcs between states are characterized by some adjustable parameters:

Version 0.4 – 28 – October 27., 2008

VauCanSon-G manual

X XAngle XCurvature XOffset

Arc 15 0.8 1pt

LArc 30 0.8 =ArcOffset

Except the curvature that depends on the size of states, parameters that define loop,

the degree of opening and the offset, are adjustable parameters.

X XAngle (degrees) XOffset

Loop 30 0pt

CLoop 22 =LoopOffset

LoopVar 28 0.7pt

2 × Angle

Offset

Likewise, one can modify the style of arrows, that are defined by three adjustable param-

eters :


EdgeArrowStyle ->

EdgeArrowWidth 5pt

EdgeArrowLengthCoef 1.4

EdgeArrowInsetCoef 0.1

LengthInset

Width

The length and the inset of arrows are given by coefficients that are applied to the

width. There exists some other (non adjustable) parameters to define arrows in spe-

cial cases: \EdgeArrowRevStyle is equal to <-, to draw transition in reverse mode; for

edges with double lines, the size of arrows is a little bit more large. It is defined by

\EdgeDblArrowWidth and \EdgeDblArrowLengthCoef that are respectively equal to 5.5pt

and 1.7.

Zigzag edges are characterized by some adjustable parameters:


ZZSize 0.9cm

ZZLineWidth 1.7

ZZSize is the apparent diameter of the zigzag and ZZLineWidth is a coefficient that is

applied to EdgeLineWidth and gives the width of the line.

Version 0.4 – 29 – October 27., 2008

VauCanSon-G manual

Transition preset parameters The default position of labels on transitions depends

on the type of transition. For instance, on edges, this position is given by the variable

\EdgeLabelPosit that is equal to 0.45. The first column of the following array gives these

values for every transition.

X \XLabelPosit \XLabelRevPosit

Edge .45 .55

Arc .4 .6

LArc .4 .6

Loop .25 .75

CLoop .25 .75

Init .1 .9

Final .9 .1

When the reverse mode is on, the position of label is given by variables that correspond

to the second column, as \EdgeLabelRevPosit for instance. For the same type of transi-

tion, the sum of both variables that defined position for straight and reverse arrows should

be equal to 1 (if one wants to keep the same appearance when using the ReverseArrow

command).

These parameters can be modified with a \renewcommand.

6 Using “plain” PSTricks commands

VauCanSon-G is a set of macros based on PSTricks. It is therefore fully compatible

with PSTricks instructions. Actually, the VCPicture environment is a specialization of

the pspicture environment; more, every state in VauCanSon-G is a PSTricks node and

every transition (loop, edge, arc) is a node connection.

The following example shows how VauCanSon-G commands can be mixed with plain

PSTricks commands. For further explanation on PSTricks, we refer to [1, 3, 4, 6].

⊕ ⊕1 0 0

0011

The shif register for 1 + x2 + x3

\begin{VCPicture}{(-7.5,-1)(3,2)}

\rput(-5,0){\rnode{X}{\psframebox{$\bigoplus$}}}% pstricks node

\rput(.5,0){\rnode{Y}{\psframebox{$\bigoplus$}}}% pstricks node

\State[1]{(-3.5,0)}{A} \State[0]{(-1,0)}{B} \State[0]{(2,0)}{C}

\Point{(-7,0)}{S}

\EdgeL{S}{X}{0011}

\EdgeL{X}{A}{} \EdgeL{A}{B}{} \EdgeL{B}{Y}{} \EdgeL{Y}{C}{}

\ncangles[angleB=90, armB=1cm]{C}{X}% pstricks connection

\ncangles[angleB=90, armB=1cm]{C}{Y}% pstricks connection

\end{VCPicture}

Version 0.4 – 30 – October 27., 2008

VauCanSon-G manual

appendix

A Version history

A first version of the package, which would be numbered 0.1, was called Vaucanson and

used by the authors in their papers between 2000 and 2003. But, at the same time, the

authors were involved, in cooperation with the LRDE at EPITA, in the design of a C++

platform for programming automata, for which it was decided that there would be no

better name than Vaucanson as well. We thus turned the name of the package for drawing

automata to VauCanSon-G.

Version 0.2 was issued in May 2003 and made available on the web together with this

user’s manual first version. A series of bug corrections and slight improvements made us

switch at some point to version 0.3.

Just before sending the package to CTAN, we undertook a full review of the code and

updated the manual accordingly. We call it version 0.4. It is the last release before a

completely new version of the package, with many more options , which is currently under

work.

Version 0.4 – 31 – October 27., 2008

VauCanSon-G manual

B Style files

B.1 slides style

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%

%% Package ‘Vaucanson-G’ version 0.4

%%

%% This is file ‘VCPref-slides’.

%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%% Scales --- slides settings

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\renewcommand{\LargeScale}{1.5}

\renewcommand{\MediumScale}{1.16}

\renewcommand{\SmallScale}{0.92}

\renewcommand{\TinyScale}{0.75}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% State aspect

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\SetStateLineColor{blue}

\SetStateLineWidth{2pt}

\SetStateFillColor{Cyan}

\SetStateLabelColor{Sepia}

\FixDimState{solid}{YellowOrange}{1}{YellowOrange}{white}

%%%%%%%%%%%%%%

% Edge aspect

%%%%%%%%%%%%%%

\SetEdgeLineColor{Mahogany}

\SetEdgeLineWidth{1.2pt}

\SetEdgeLabelColor{OliveGreen}

%%% Dimmed edges

\FixDimEdge{dashed}{1.2}{Apricot}{Apricot}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

Version 0.4 – 32 – October 27., 2008

VauCanSon-G manual

B.2 beamer style

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%


%%

%% This is file ‘VCPref-slides’.

%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%% Scales --- slides settings

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\renewcommand{\LargeScale}{0.85}

\renewcommand{\MediumScale}{0.6}

\renewcommand{\SmallScale}{0.4}

\renewcommand{\TinyScale}{0.30}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% State aspect

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\SetStateLineColor{blue}

\SetStateLineWidth{2pt}

\SetStateFillColor{Cyan}

\SetStateLabelColor{Sepia}

\FixDimState{solid}{YellowOrange}{1}{YellowOrange}{white}

%%%%%%%%%%%%%%

% Edge aspect

%%%%%%%%%%%%%%

\SetEdgeLineColor{Mahogany}

\SetEdgeLineWidth{1.2pt}

\SetEdgeLabelColor{OliveGreen}

%%% Dimmed edges

\FixDimEdge{dashed}{1.2}{Apricot}{Apricot}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

Version 0.4 – 33 – October 27., 2008

VauCanSon-G manual

B.3 mystyle style

This file is given only on the purpose that it can be edited by the user and called by the

option mystyle of the wrapper(and this is the reason why the name VCPref-mystyle.tex

of this file should not be changed).

The actual values given in this file as an example provide a style which mimics the

way automata are drawn with GasTeX [2] as can be witnessed below.

A

B

C

D

a

b

c

d

a′

b′

c′

d′

\input{VCPref-mystyle}

\VCDraw{%


% states

\State[A]{(0,0)}{A} \State[B]{(2,-2)}{B}

\FinalState[C]{(4,2)}{C} \State[D]{(6,0)}{D}

%initial-final

\Initial{A} \Final[s]{B}

% transitions


\LArcR{B}{D}{c} \LArcL{C}{D}{d}

\ArcL{A}{B}{a’} \EdgeLineDouble \EdgeR{A}{C}{b’}

\EdgeLineSimple \EdgeL{B}{D}{c’} \LArcR{C}{D}{d’}

%

\end{VCPicture}}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%


%%

%% This is file ‘VCPref-mystyle’.

%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%% Scales ---

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\renewcommand{\LargeScale}{1.2} %float : argument of a \scalebox

\renewcommand{\MediumScale}{1} %float

\renewcommand{\SmallScale}{.7} %float

\renewcommand{\TinyScale}{0.5} %float

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%% State parameters --- Default settings

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\setlength{\LargeStateDiameter}{1.2cm} %length

\setlength{\MediumStateDiameter}{.8cm} %length

\setlength{\SmallStateDiameter}{.6cm} %length

\renewcommand{\StateDblDimen}{outer}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% State aspect

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\SetStateLineWidth{.14mm} %% length

\SetStateFillStatus{none} %% aspect

Version 0.4 – 34 – October 27., 2008

VauCanSon-G manual

\SetStateFillColor{black} %% color

\SetStateLabelScale{1} %% float

\FixStateLineDouble{2}{5} %% Double style:

%%%%%%%%%%%%%%

% Edge aspect

%%%%%%%%%%%%%%

\SetEdgeLineWidth{.14mm} %% length

\SetEdgeLabelColor{black} %% color

\SetEdgeLabelScale{1} %% float

\FixEdgeLineDouble{1.5}{2} %% float :

%%% arrows

\SetEdgeArrowWidth{1.03mm} %width of the edge arrow

\SetEdgeArrowLengthCoef{1.37} %float :

\setlength{\EdgeDblArrowWidth}{1.3mm} %width :

\renewcommand{\EdgeDblArrowLengthCoef}{1.09} %

\SetEdgeArrowInsetCoef{0} %float : coef*\EdgeArrowSizeDim

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Arc geometry

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\SetArcAngle{17} %% int (degree)

\SetLArcAngle{30} %% int (degree)

\SetArcCurvature{0.7} %% float

\SetArcOffset{1pt} %% length

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Loop geometry

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\renewcommand{\LoopOnLargeState}{5.5} %float

\renewcommand{\LoopOnMediumState}{7} %float : curvature

\renewcommand{\LoopOnSmallState}{9} %float

\renewcommand{\LoopOnVariableState}{4.5} %float

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%% Edge labels positionning

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\renewcommand{\EdgeLabelPosit}{.5} %per cent

\renewcommand{\EdgeLabelRevPosit}{.5}

\renewcommand{\ArcLabelPosit}{.5}

\renewcommand{\ArcLabelRevPosit}{.5}

\renewcommand{\LArcLabelPosit}{.5}

\renewcommand{\LArcLabelRevPosit}{.5}

\renewcommand{\LoopLabelPosit}{.5}

\renewcommand{\LoopLabelRevPosit}{.5}

\renewcommand{\CLoopLabelPosit}{.5}

\renewcommand{\CLoopLabelRevPosit}{.5}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%% Initial states parameters

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\renewcommand{\ArrowOnMediumState}{1} %float

\renewcommand{\ArrowOnSmallState}{1} %float

\renewcommand{\ArrowOnLargeState}{1} %float

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

Version 0.4 – 35 – October 27., 2008

VauCanSon-G manual

References

[1] D. Girou Presentation de PSTricks, Cahier GUTenberg 16 (1994) 21-70.

[2] P. Gastin GasTeX: Graphs and Automata Simplified in TeX.

http://www.lsv.ens-cachan.fr/ gastin/gastex/gastex.html

[3] M. Goossens, S. Rahtz and F. Mittelbach The LaTeX Graphics Companion.

Addison Wesley, 1997.

[4] M. Goossens, S. Rahtz, F. Mittelbach, D. Roegel, and H. Voss The LaTeX

Graphics Companion, 2nd Edition. Addison Wesley, 2007.

[5] J. Sakarovitch, Elements de theorie des automates. Vuibert, 2003. Eng. trans.

Elements of Automata Theory. Cambridge University Press, to appear.

[6] H. Voss, PSTricks – Grafik fur TeX und LaTeX. Lehmanns/Dante e.V., 4th ed.

2007.

Some examples of articles or slides that contain automata drawn with VauCanSon-G

can be found at the following URLs:

• http://www.enst.fr/∼∼∼jsaka/

• http:///igm.univ-mlv.fr/∼∼∼lombardy/

Version 0.4 – 36 – October 27., 2008

VCManual.pdf

Documents

Transcript of VCManual.pdf